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Thread: Novel Redshift Equation

  1. #31
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    Quote Originally Posted by Reality Check View Post
    Proper distance is the distance that we actually measure.
    Through what means do we measure extra-galactic proper distance?

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    The Cosmic distance ladder is something you should already know about since learning about the mainstream is part of the process of creating an against the mainstream idea. You should certainly know how Hubble measured extra-galactic proper distance (Cepheid variable stars) given the number of times that I have cited Hubble's law.
    Last edited by Reality Check; 2017-Mar-27 at 09:02 PM.

  3. #33
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    Quote Originally Posted by Reality Check View Post
    The Cosmic distance ladder is something you should already know about since learning about the mainstream is part of the process of creating an against the mainstream idea. You should certainly know how Hubble measured extra-galactic proper distance (Cepheid variable stars) given the number of times that I have cited Hubble's law.
    Cepheid Variables are based on measurements on apparent magnitude, and knowledge of absolute magnitude. How is it not a measurement of luminosity distance that this method yields?

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    Quote Originally Posted by Reality Check View Post
    The Cosmic distance ladder is something you should already know about since learning about the mainstream is part of the process of creating an against the mainstream idea.
    To clarify this statement: while it is certainly a very, very good idea to understand the mainstream science you seek to modify or overturn, our rules do not require prerequisite knowledge of it. On the other hand, the ATM forum is not the place to ask for instruction about mainstream theories. You can ask questions in the Q&A forum where you'll get mainstream answers that you may not dispute on an ATM basis. This thread is about your claims and your defense of them.
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  6. #36
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    We can get recessional velocity V_r from this alternate model with this form:



    then using hubble's law, we can divide this speed by H_o to yield Proper distance.



    So there's Proper Distance. I've graphed them out to z=10 against the equation from conventional cosmology: recessional velocity, Proper Distance

    Realitycheck, I believe you are in error about the measurability of proper distance on extragalactic scales:

    "With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance."

    "While the Hubble law distance is in principle measurable, the need for helpers all along the chain of galaxies out to a distant galaxy makes its use quite impractical. Other distances can be defined and measured more easily."

    Hubble's law is also an approximation that doesn't accurately describe our universe observationally on large scales. The Proper distance that you are referencing is absent from the cosmology calculators and is not defined mathematically in the wikipedia articles that you are linking. Maybe proper distance=luminosity distance in gravitationally bound regions, but if you are measuring luminosity, as is the case in virtually every extra-galactic measurement technique including cepheids, you are yielding luminosity distance.

    , again, note the D_l.

  7. #37
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    Quote Originally Posted by substitutematerials View Post
    ...then using hubble's law,
    That is where you go wrong making the post moot. Hubble's law is derived from mainstream cosmology and matches empirical evidence. It is not valid in a universe where galaxies are receding away from us at the speed of light which is your ATM idea.
    It is the empirical Hubble's law that states that your ATM idea is wrong because all galaxies do not recede from us at the speed of light: v = HD where v varies with distance.

    ETA: Starting with a formula that seems to appear from nowhere is not wise.
    Last edited by Reality Check; 2017-Mar-29 at 03:13 AM.

  8. #38
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    Quote Originally Posted by substitutematerials View Post
    Realitycheck, I believe you are in error about the measurability of proper distance on extragalactic scales:
    Your links do not show that proper distances on extragalactic scales cannot be measured or are wrong.: cosmic distance ladder.
    The Ned Wright page you cited has:
    Many Distances
    With the correct interpretation of the variables, the Hubble law (v = HD) is true for all values of D, even very large ones which give v > c. But one must be careful in interpreting the distance and velocity. The distance in the Hubble law must be defined so that if A and B are two distant galaxies seen by us in the same direction, and A and B are not too far from each other, then the difference in distances from us, D(A)-D(B), is the distance A would measure to B. But this measurement must be made "now" -- so A must measure the distance to B at the same proper time since the Big Bang as we see now.
    Hubble's law is an approximation that accurately describes our universe observationally on large scales. There are deviations from it which is why we say that the expansion of the universe is accelerating.

  9. #39
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    Quote Originally Posted by Reality Check View Post
    ...a universe where galaxies are receding away from us at the speed of light which is your ATM idea.
    This is not my idea Realitycheck, I'm afraid you are misunderstanding it. It's my job to clearly explain it here. I am not claiming that all galaxies are receding away from us at the speed of light- this is not a defensible position. The universe as a whole is expanding at c.

    Picture actors on an expanding stage. The stage always grows its radius at 1 foot/second. The actors do not all move apart from each other at 1 foot/second just because the stage overall is adding a foot to it's radius each second. Any actor sees themselves as the lead at center stage, of course, and they see the other actors tending to drift away from them at a rate proportional to their separation on the stage. Actors close enough to each other can even hold hands and avoid drifting apart at all. An actor on the edge of the stage will drift away at the full rate of one foot/second.

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    Quote Originally Posted by substitutematerials View Post
    This is not my idea Realitycheck, I'm afraid you are misunderstanding it. It's my job to clearly explain it here. I am not claiming that all galaxies are receding away from us at the speed of light- this is not a defensible position. The universe as a whole is expanding at c.

    Picture actors on an expanding stage. The stage always grows its radius at 1 foot/second. The actors do not all move apart from each other at 1 foot/second just because the stage overall is adding a foot to it's radius each second. Any actor sees themselves as the lead at center stage, of course, and they see the other actors tending to drift away from them at a rate proportional to their separation on the stage. Actors close enough to each other can even hold hands and avoid drifting apart at all. An actor on the edge of the stage will drift away at the full rate of one foot/second.
    I had this idea exactly, however I took Perlmutters SN data and I found it to be false.
    I took his redshift data and calculated the proper distance to each event.
    What I found was that the further the event, the bigger the difference to the expected result.
    I had to add a lorentz factor and muliply it by 6 to get a good fit...

    Cheers
    L-zr

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    Quote Originally Posted by Lazer View Post
    I had this idea exactly, [...]
    This thread is not about your idea. If you have an alternative theory to advocate and defend, please start your own thread.
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    Quote Originally Posted by PetersCreek View Post
    This thread is not about your idea. If you have an alternative theory to advocate and defend, please start your own thread.
    Jeees we are really sensitive aren't we, If you read properly you can read that I state it was false...

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    Quote Originally Posted by Lazer View Post
    Jeees we are really sensitive aren't we, If you read properly you can read that I state it was false...
    Yes, we are. It is also against our rules to comment on or argue with moderation in thread. If you wish to comment back about moderation, PM the moderator (if you'd like to do it in private) or in Feedback if you want to do it publicly.
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  14. #44
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    Quote Originally Posted by substitutematerials View Post
    ...The universe as a whole is expanding at c.
    I know that is your idea. The effect (unless you can show otherwise) of asserting that the "universe as a whole is expanding at c" is that distances in the universe are expanding at a constant velocity. That means that galaxies will be getting further apart from each other at a constant velocity (maybe the speed of c).

    Your picture implies an idea about a universe that is expanding by adding to its outside only but then galaxies do not move apart at all!
    However add the word "rubber" to the stage properties. The actors move apart from each other at a constant velocity because all of the stage is expanding at a constant velocity.
    Last edited by Reality Check; 2017-Mar-30 at 08:59 PM.

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    Quote Originally Posted by substitutematerials View Post
    This is not my idea Realitycheck, I'm afraid you are misunderstanding it. It's my job to clearly explain it here. I am not claiming that all galaxies are receding away from us at the speed of light- this is not a defensible position. The universe as a whole is expanding at c.

    Picture actors on an expanding stage. The stage always grows its radius at 1 foot/second. The actors do not all move apart from each other at 1 foot/second just because the stage overall is adding a foot to it's radius each second. Any actor sees themselves as the lead at center stage, of course, and they see the other actors tending to drift away from them at a rate proportional to their separation on the stage. Actors close enough to each other can even hold hands and avoid drifting apart at all. An actor on the edge of the stage will drift away at the full rate of one foot/second.
    The problem with this is that it assumes that the universe has a finite (known) radius centered on the Earth.

    There is no reason to think that the observable universe (parts of which are receding from us faster than c, contrary to your idea) is the entire universe.

    In your model the scale factor would change over time. This, again, is not what we observe.

    There is good evidence to suggest that the universe is much larger than the observable universe (again, contrary to your idea).

    It seems extremely odd to suggest that we are at the centre of the universe. It is normally only a small group of religious fundamentalists who hold to such a view.

  16. #46
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    Quote Originally Posted by Reality Check View Post
    I know that is your idea. The effect (unless you can show otherwise) of asserting that the "universe as a whole is expanding at c" is that distances in the universe are expanding at a constant velocity. That means that galaxies will be getting further apart from each other at a constant velocity (maybe the speed of c).

    Your picture implies an idea about a universe that is expanding by adding to its outside only but then galaxies do not move apart at all!
    However add the word "rubber" to the stage properties. The actors move apart from each other at a constant velocity because all of the stage is expanding at a constant velocity.
    Define a coordinate system by it's relationship to the edge of the stage, by hooking a tape measure to the edge and reading the measurement at the center of the stage. Each second, the tape measure must register a foot of growth. The measurement made one second ago will now be one foot away from the actor who is reading it. This is the analogy to the propagation of light. Light remains static in this coordinate system: for a photon, the distance to the edge remains the same, and no time elapses.
    I agree that in some way the analogy works better if you picture the observer on the the edge of the stage, static in relation to the center of the stage, so the growing stage is passing beneath them at 1 foot per second- but its only an analogy.

  17. #47
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    Quote Originally Posted by Strange View Post

    The problem with this is that it assumes that the universe has a finite (known) radius centered on the Earth.

    There is no reason to think that the observable universe (parts of which are receding from us faster than c, contrary to your idea) is the entire universe.

    In your model the scale factor would change over time. This, again, is not what we observe.


    It seems extremely odd to suggest that we are at the centre of the universe. It is normally only a small group of religious fundamentalists who hold to such a view.

    I am not proposing a change to the scale factor we observe, remember? Time dilation intrinsically results from a constant growth universe. It is given by and can be transformed in to co-moving or constant time coordinates: the evolution of scale (a) is defined by 1/1+z, and the co-moving distance is the integral of scale. Again, a recessional velocity in this coordinate system can be greater than c. This works well for the observations I've compared it to. I'm very open to contrary evidence.

    I don't think I'm claiming the Earth is at the objective geographic center of the universe simply by claiming that the universe is finite. All observers at all times perceive themselves at the center of the universe, this is relativistic just like conventional cosmology.

    Quote Originally Posted by Strange View Post
    There is good evidence to suggest that the universe is much larger than the observable universe (again, contrary to your idea).
    This is a good challenge to this model. The principle piece of evidence that the universe is larger than the observable universe that I know of is the extreme flatness we observe. Can you help with the other observational evidences that suggest it is much larger? Regarding flatness, most people seem to agree that this rules out the Milne universe, which should appear extremely curved. My model defers from the Milne universe in that it equates light's propagation with spatial expansion, and I think this makes flatness apriori- it's like trying to measure an angle with a floppy protractor that conforms to the thing its supposed to measure, it can't be done.

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    Quote Originally Posted by substitutematerials View Post
    I am not proposing a change to the scale factor we observe, remember? Time dilation intrinsically results from a constant growth universe. It is given by and can be transformed in to co-moving or constant time coordinates: the evolution of scale (a) is defined by 1/1+z, and the co-moving distance is the integral of scale.
    I don't see how time dilation "intrinsically results" from a constant growth universe. This appears to be an ad-hoc assumption to make the maths work (assuming it does work, I haven't looked at it in enough detail to know).

    I don't see how that solves the problem that a horizon moving away at a constant speed will mean that the amount by which the universe is scaling decreases over time.

    I don't think I'm claiming the Earth is at the objective geographic center of the universe simply by claiming that the universe is finite. All observers at all times perceive themselves at the center of the universe, this is relativistic just like conventional cosmology.
    I though that your horizon that is receding at c is the "edge" of the universe. So, presumably, someone who is, say, 12 billion light years from us (light travel time; I don't know what that would mean in terms of roper distance in your model) would only be 1 billion light years from the edge. Why would they see isotropic expansion? They would see something very different in direction than the other.

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    Quote Originally Posted by substitutematerials View Post
    Define a coordinate system by it's relationship to the edge of the stage,...
    That would be a rather ignorant change for the analogy because
    1. The universe has no evidence of an "edge".
      We have a limit to how far we can observe (the observable universe). There is evidence that the universe is much bigger than the observable universe. Thus the stage should be infinite.
      If we assume a finite universe then there still is no edge - we have the balloon analogy instead.
    2. This is adding a magic tape measure that is unaffected by the expanding stage.
      Tape measures will be embedded in that stage and get bigger as it expands.

    An analogy is not an answer to:
    IF01: Derive the relationship between redshift and distance of galaxies in a universe expanding at the speed of light.

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    Quote Originally Posted by Strange View Post
    I don't see how time dilation "intrinsically results" from a constant growth universe. This appears to be an ad-hoc assumption to make the maths work (assuming it does work, I haven't looked at it in enough detail to know).
    It's not ad hoc- the math comes out of the idea, as in the vinyl record analogy I gave earlier in the thread. If light is stationary with respect to expanding space, and only propagates because of spatial expansion, it's like playing a vinyl record by stretching it instead of spinning it- playback of distant events will be slowed down.

    Quote Originally Posted by Strange View Post
    I though that your horizon that is receding at c is the "edge" of the universe. So, presumably, someone who is, say, 12 billion light years from us (light travel time; I don't know what that would mean in terms of roper distance in your model) would only be 1 billion light years from the edge. Why would they see isotropic expansion? They would see something very different in direction than the other.
    In light travel distances like you are giving, your question is easy. If we look at someone 12 billion light years away from us, and thus perceive them as 1.75 billion lightyears (light travel distance again) from the horizon, we are also seeing them as they were 12 billion years ago, when the D_lt radius of the universe was 1.75 billion light years. So our measurement of their distance from horizon would agree with their measurement of their distance from the horizon, even though they perceive themselves to be at the center of an isotropically expanding universe- it's an earlier, smaller universe.

    The observer and emitter do not seem to agree about the comoving distance of the emitter to the horizon though- the galaxy has a lookback time of 12 billion years, so my equations yield a comoving distance from us of 27.25 glyr for that galaxy, or a distance of 26.66 glyr to the horizon. Since we are seeing them as they were at a cosmic time of 1.75 gyr, their measured distance to the horizon would have been 6.86 glyr.

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    Quote Originally Posted by Reality Check View Post
    There is evidence that the universe is much bigger than the observable universe.
    Like I said to Strange, evidence that the universe is much larger than ~54 glyr in radius would be a good challenge to my model. Can we talk about the observational evidence that suggests this? I've already mentioned spatial flatness and given a explanation for it. What are the other observations suggesting a very large or infinite universe that this model needs to account for?

    We imagine we can agree that there are 3 basic possibilities for the extent of the universe:
    infinite
    finite and unbounded
    finite and bounded

    each of these possibilities is hard to think about but none have been definitively ruled out. I am arguing for a model in which a boundary in time (a beginning) creates a boundary in space. A finite volume has expanded at a finite rate for a finite amount of time.

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    Quote Originally Posted by substitutematerials View Post
    Like I said to Strange, evidence that the universe is much larger than ~54 glyr in radius would be a good challenge to my model.
    Oh good - an actual number from your model!
    IF02: Please show your calculation of a greater than ~54 glyr radius which would invalidate your model.

    Size of the observable universe (radius = 46 billion light-years).

    We have known for a decade or so that the evidence is that the universe is very close to flat which means that the whole universe is much bigger than the observable universe.
    How Big is the Entire Universe? (2012 article)
    So it goes with the Universe as well. We were able to measure that the Universe, if it is curved, has a much larger radius of curvature than that of our observable Universe, which is about 46 billion light years. But if we could make that measurement more precise, we could conceivably measure a much smaller curvature than even that. Thanks to the WMAP satellite, we now have the temperature fluctuations over the entire sky measured at a very narrow, less-than-half-a-degree resolution.
    And what they teach us is that not only is the Universe consistent with being flat, itís really, really, REALLY flat! If the Universe does curve back and close on itself, its radius of curvature is at least 150 times as large as the part thatís observable to us! Meaning that ó even without speculative physics like cosmic inflation ó we know that the entire Universe extends for at least 14 trillion light years in diameter, including the part thatís unobservable to us today.
    Planck measurements of the CMB puts even tighter constraints on the curvature of the universe

  23. #53
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    Quote Originally Posted by Reality Check View Post
    Oh good - an actual number from your model!
    IF02: Please show your calculation of a greater than ~54 glyr radius which would invalidate your model.


    1/2.311E-18=4.327E17
    4.327E17/31536000=13.721E9 years



    13.21E9 lyr(1+2.9207/1)= 53.796E9 lightyears.

    Observations from beyond this distance should not be possible in the model, since z goes to infinity at this horizon, meaning time is infinitely dilated (stopped) from our perspective at t_o.

    There are some other actual numbers in this thread in post #1 and #17.

    Quote Originally Posted by Reality Check View Post

    Size of the observable universe (radius = 46 billion light-years).

    We have known for a decade or so that the evidence is that the universe is very close to flat which means that the whole universe is much bigger than the observable universe.
    How Big is the Entire Universe? (2012 article)

    Planck measurements of the CMB puts even tighter constraints on the curvature of the universe
    As I said, I don't think measurements of spatial curvature are possible if light is propagated by spatial expansion; the tool with which you are measuring the curvature with is curving right along with it. The extreme flatness we observe should be regarded as a failed prediction of FLRW space, since it is very improbable for mass-energy to be so precisely balanced to the critical density to produce this flatness. We need inflation added to the model to produce this region of balanced density. An alternative is just that space on the largest scales is Euclidean apriori.

    Is there anything other than the measurement of flatness that indicates the universe is much larger than 54 glyr?

    Thanks for your time as always.

  24. #54
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    Quote Originally Posted by substitutematerials View Post
    ...
    An equation from your model thus gives a number that debunks your model , substitutematerials !

    Your personal opinion does not make the cosmology in How Big is the Entire Universe? (2012 article) invalid. Especially coupled with what seems to be ignorance about what the article contains. WMAP and Planck are not "tools" used to measure curvature. They measure the CMB. Working cosmology models which include the FLRW metric are used to match the observed data. They show that the observed universe is very close to or maybe exactly flat. Exactly flat suggests an infinite universe. Close to flat gives a universe vastly bigger than the observable universe which has a measured radius of 46 billion light-years.

    This hints at a couple of more questions (not formal yet): Can you show that the measurements of flatness are wrong? Can you match the CMB data with your model?

    The measurement of flatness remains evidence that the radius of the universe is at least 7 trillion light years. 7 trillion is greater then 54 billion.

    P.S. IF01: Derive the relationship between redshift and distance of galaxies in a universe expanding at the speed of light.
    Last edited by Reality Check; 2017-Apr-05 at 11:04 PM.

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    Quote Originally Posted by Reality Check View Post
    Can you match the CMB data with your model?
    Evaluating the CMB, we can relate temperature to redshift by


    if the surface of last scattering was 2975 K and the present CMB is 2.73 K, redshift of the CMB is 1089. In my model z= 1089 gives a lookback time of 0.999957 versus 0.999972 in LCDM via the Cosmocalc. These differ by 1/1000th of a percent, and give a time of emission for the CMB of 590,000 years versus 380,000 years in LCDM.

    As I understand it, the most important cosmological probe gleaned from the CMB is a measurement of the sound horizon of Baryon Acoustic Oscillations. We can measure the average angular size of this acoustic scale, and it should correspond to a preferred separation distance of galaxies in the present day- which tells us if our model computes the evolution of scale correctly.

    We can compute angular size distance (d_A) for z=1089 by



    and again, compare to the Cosmocalc, we get .04793 glyr using my equations and 0.04174 glyr using the cosmocalc for the z of 1089 that would correspond to the surface of last scattering. The difference between these values is ~13%.

    The sound horizon of BAOs in the CMB has been measured by Planck be:



    Using



    We get a sound horizon of 166.95 Mpc from my alternative model, versus 144.71 Mpc for Planck and LCDM, again a disagreement of around 13%. Other values out there seem to center around ~150 Mpc. The value computed from my model given Planck's angular measurement seems to be amongst the highest. I am not familiar enough with the field to say if it is disqualifyingly high. The real test of a model is how well the sound horizon measurement agrees with modern galaxy separation, and this graph
    Click image for larger version. 

Name:	Galaxy separation arxiv.org1312.4877.jpg 
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    suggests that there are fairly large error bars and uncertainty in determining this, and furthermore the study it is from seems to point to a value larger than 150 mpsc. Perhaps the discrepancy is enough to be considered as a test though.


    I'm not sure what would satisfy this request for you. The equation being presented here works better than the Hubble law relation. In this theory, redshift is fundamentally determined not by distance of separation but by relative time of separation. Past galaxies are time dilated, and this can be transformed into a scaling of distance, which can be framed as a recessional velocity. Hubble's law happens to work on moderate distances because distance and lookback time are very similar for the recent past- the quantities diverge on larger scales.

    The key thing here is that the scale factor is the heart of either cosmology, and this evolution of scale is quantitatively very close between the mainstream model and this alternative. Ultimately, we are talking about a change in scale over time. Even if my model is totally batty, is a very good heuristic without any free parameters. Again, I welcome a better one.

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    Quote Originally Posted by substitutematerials View Post
    Evaluating the CMB, we can relate temperature to redshift by ...
    Redshift is irrelevant to the CMB so you obviously did not understand the informal question. So I will make it formal:
    IF03a: Please derive the temperature of the CMB from your model.
    IF03b: Please derive the variation of temperature of the CMB with distance from your model.
    IF03c: Please derive the spectrum of the CMB from your model.
    IF03d: Please derive the power spectrum of the CMB from your model.
    Remember that a valid answer is that your model cannot do this.

    What would answer
    IF01: Derive the relationship between redshift and distance of galaxies in a universe expanding at the speed of light.
    would be an answer that is relevant !
    As I stated on 2017-Mar-26: The answer will be a function of z (redshift) and D (proper distance) or recessional velocity vr and D (as in Hubble's law). That will give a relationship that can be compared with measurements of z or v[SUB]r and measured distances to galaxies.

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    Quote Originally Posted by Reality Check View Post
    Redshift is irrelevant to the CMB
    I'm sorry but this is quite wrong. Without redshift (z) the Cosmic Microwave Background would not be the Cosmic Microwave Background, it would be the Cosmic Visible Light Background. Redshift is everything to the CMB. In fact without the change in scale (a) that redshift is counterpart to, the universe never even would have cooled enough for the CMB photons to escape the primordial plasma. What do you mean it is irrelevant?

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    Quote Originally Posted by substitutematerials View Post
    What do you mean it is irrelevant?
    Your post starting "Evaluating the CMB, we can relate temperature to redshift ..." is irrelevant to what I asked. The mainstream expanding universe has predictions that match the measured temperature of the CMB, etc. A universe expanding at the speed of light for the age of the universe might not match the data. Thus
    IF03a: Please derive the temperature of the CMB from your model.
    IF03b: Please derive the variation of temperature of the CMB with distance from your model.
    IF03c: Please derive the spectrum of the CMB from your model.
    IF03d: Please derive the power spectrum of the CMB from your model.
    Last edited by Reality Check; 2017-Apr-10 at 02:23 AM.

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    Because the scale factor evolves almost identically in the alternate model, we can derive the temperature of the CMB in the same way as in conventional cosmology.

    plasma physics shouldn't change. Both temperature and density are functions of z, and so in equations were they are employed such as in the Saha equation, the alternate model will match the conventional. The complete set of calculations to determine when the temperature at which electrons and protons have combined enough to be effectively transparent are complicated, but as scale changes almost identically, anything dependent on scale will be the same.

    In fact, the temperature evolution of the alternative equation works all the way down the planck time. Compare the history of temperature from conventional cosmology
    to calculations using this form:

    (-ln(t/4.3E17)/sqrt(1-(1-t/4.3E17)^2))*2.73

    at http://keisan.casio.com/calculator


    input (t) in seconds and you will get temperature in Kelvins.

    Going further, because this temperature and density evolution is the same as conventional cosmology, big bang nucleosynthesis has a comparable amount of time to elapse, from around 1 second at 10^10 K to around 100 seconds at 10^9 K. Baryogenesis occurs around the same time. The temperature at the planck time is 10^32K, isn't this a note-worthy fit?!

    if you mean extrapolating the scale of inhomogenity from the angular size of the acoustic scale of the CMB, please refer to my post #55.


    This is still a big bang cosmology, with the universe beginning in a hot dense state. The spectrum of the CMB should be blackbody for a gas in thermal equilibrium filling space uniformly. As far as i understand, this model still has the standard horizon problem, where regions of space that were no longer causally connected at the time of last scattering are almost perfectly equilibriated,

    Because spatial expansion is not a function of spatial separation in this model, but rather a linear function of time, there is an initial window of time when the universe and the scale factor expand faster than exponentially. However based on my back of the envelope calculations, this growth appears to be slower than the efoldings required by inflationary models, so I would expect a horizon problem to remain.

    This is out of my league, I'm afraid. I can tell you that there is no reason to assume a different density of baryons, dark matter or radiation as a function of the critical density from presently accepted values. So the acoustics of these quantities should remain the same. In as much as the primordial fluctuations come out of quantum mechanics and inflation, I cannot bring anything to bear.

    Note that I am claiming that the critical density itself is not a meaningful number- the dark energy component is absent in my model, and space will appear globally flat (not locally of course) no matter what the overall density of mass energy is.

  30. #60
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